WO2023198550A1

WO2023198550A1 - Multi-shaft screw machine comprising a pair of screw elements having an improved mixing and degassing effect with reduced energy input

Info

Publication number: WO2023198550A1
Application number: PCT/EP2023/058951
Authority: WO
Inventors: Thomas Koenig; Michael Bierdel
Original assignee: Covestro Deutschland Ag
Priority date: 2022-04-11
Filing date: 2023-04-05
Publication date: 2023-10-19

Abstract

The present invention relates to a pair of screw elements suitable for a multi-shaft screw machine, comprising: m screw shafts SW₁ to SW_m, which rotate in the same direction and at the same speed and the adjacent rotational axes X₁ to X_m of which have an axial spacing A in a cross section at a right angle to the rotational axes; and m circular housing bores, which pass into one another and each have an identical housing bore internal diameter D, and the bore midpoints M₁ to M_m of which have a spacing identical to the axial spacing A, and the bore midpoints M₁ to M_m of which coincide with the respective associated rotational axes X₁ to X_m of the screw shafts SW₁ to SW_m and with the rotational midpoints P₁ to P_m of the screw elements; wherein: the two screw elements of the pair of screw elements are opposite each other on directly adjacent screw shafts; the two screw elements of the pair of screw elements scrape against each other with a screw element clearance s; both screw elements have an asymmetrical screw profile; both screw elements have precisely two flight lands; for each of the two screw elements, the two flight lands thereof have different spacings from the respective rotational midpoint P of the screw profile.

Description

MULTI-SHAFT SCREW MACHINE WITH A PAIR OF SCREW ELEMENTS WITH IMPROVED MIXING AND DEGASSING EFFECT WITH REDUCED ENERGY INPUT

The subject of the present invention is a pair of screw elements, _suitable for a multi-shaft screw machine with m screw shafts SWi to SW _m rotating in the same direction and at the same speed, the respective adjacent axes of rotation X ₁ to penetrating, circular housing bores, each of which has an identical housing bore inner diameter D and whose bore centers M ₁ to M _m have a distance that is equal to the center distance A, and whose bore centers M ₁ to M _m with the respective associated axes of rotation X ₁ to X _m Worm shafts SWi to SW _m and coincide with the centers of rotation P ₁ to P _m of the screw elements, the two screw elements of the pair of screw elements lying opposite one another on immediately adjacent screw shafts, the two screw elements of the pair of screw elements scraping each other with a play between screw element and screw element s, wherein both screw elements have an asymmetrical screw profile, both screw elements each having exactly two combs, with each of the two screw elements having its two combs at different distances from the respective center of rotation P of the screw profile, with each comb having a distance D/2 reduced by a play between the screw element and the housing wall 5 and further reduced by an additional gap SP to the respective center of rotation P and the other comb has a distance D/2 reduced by a play between the screw element and the housing wall 5, but not reduced by an additional gap SP, to the respective center of rotation P has, whereby for both screw elements the clearance between screw element and housing wall 5 is the same and for both screw elements the additional gap SP is the same, whereby the equation applies to the sum of the comb angles of both screw elements BKW in radians

BKW = ƒ * BKGW (1) fulfilled where for the factor ƒ the factor ƒ is greater than 0 and less than or equal to 0.95, where BKGW is determined by:

The parameters required to represent a screw profile are listed below in Table 1.

In WO 2011/006516A1 an extruder with a housing with at least two axially parallel shafts that can be driven in the same direction is disclosed, which are provided with at least two-threaded conveyor elements which strip each other at an axial distance with little play over the entire circumference, with between the comb of at least one further There is a distance (a) between the corridor and the inner wall of the housing.

A multi-shaft screw machine is known from EP0875356A2. The multi-shaft screw machine is provided with a housing, with two mutually parallel, partially penetrating housing bores, with two rotatable shafts arranged in the housing bores, with screw elements mounted on the shafts in a rotationally fixed manner and with kneading disks that mesh with one another in a rotationally fixed manner on the shafts are each narrowed in their comb areas compared to the disc width (B) to form mixing and scraper pins located on the circumference.

Furthermore, from DE 10 2008 016862 A1 there is an extruder with at least two axially parallel shafts that can be driven in the same direction and which has at least two-threaded conveying elements (2, 11, 12) which essentially come into close contact with one another at one point (C).

EP 0 788 868 A1 describes a method and a device for mixing thermoplastic material with continuous rollers. The device has a mixing chamber and at least one pair of threaded shafts arranged within the mixing chamber (5), the threaded shafts having at least a tip portion of the thread and at least a core portion of the thread which are asymmetrical with respect to the longitudinal axis of the shaft are lowered to create surfaces of the shafts and an empty space between the countersunk threaded portion and the inner surface of the chamber to perform rolling of the material on at least a portion of the surface of the chamber itself during the feeding of the material to the outlet of the mixing chamber.

Furthermore, WO 2016/107527 A1 discloses a self-cleaning extrusion device with two synchronous screws. The device consists of a screw mechanism, a cylinder, a feed port, a vent port and an outlet port.

For the purposes of the present invention, a multi-shaft screw machine is understood to mean a screw machine with more than one screw shaft, for example a screw machine with two, three or four screw shafts or an extruder with eight to sixteen, in particular twelve, screw shafts arranged in a ring. If there are more than two screw shafts, the axes of rotation of the screw shafts can be arranged next to one another or, for example - as in a so-called ring extruder - in a ring shape relative to one another. In multi-screw extruders, the axes of rotation of the screw shafts are usually arranged parallel to one another. This parallel arrangement of the axes of rotation is also preferred according to the invention. The screw elements of the pair of screw elements according to the invention are preferably arranged directly opposite one another on the screw shafts in a number that corresponds to the number of screw shafts of the respective extruder. Such a screw machine with more than one screw shaft is also referred to below as a multi-screw screw machine, multi-screw screw machine or multi-screw extruder. A twin-screw screw machine is also referred to below as a twin-screw extruder. For the purposes of the present invention, the term “screw machine” is used synonymously with the term “extruder”. An extruded mass or mass to be extruded is also referred to below as “extrudate”.

The multi-shaft screw machine is preferably a twin-screw extruder with two screw shafts SWi to SW2 rotating in the same direction and at the same speed, with adjacent axes of rotation X ₁ and X ₂ , bore centers M ₁ and M ₂ and centers of rotation P ₁ and P ₂ .

In the context of the present invention, an extrudate is a plastic or viscoelastic mass, in particular selected from the group comprising the members: suspensions, pastes, glass melts, unfired ceramics, metal melts, or plastics.

For the purposes of the present invention, plastics are understood to mean in particular: polymers, in particular polymer melts or polymer solutions, again in particular melts or solutions of thermoplastic polymers or melts or solutions of elastomers, especially rubbers.

The preferred thermoplastic polymer is at least one from the series polycarbonate, polyester carbonate, polyamide, polyester, in particular polybutylene terephthalate and polyethylene terephthalate, polylactide, polyether, thermoplastic polyurethane, polyacetal, fluoropolymer, in particular polyvinylidene fluoride, polyether sulfones, polyolefin, in particular polyethylene and polypropylene, polyimide, polyacrylate, in particular poly(methyl) methacrylate, polyphenylene oxide, polyphenylene sulfide, polyether ketone, polyaryl ether ketone, styrene polymers, in particular polystyrene, styrene copolymers, in particular styrene-acrylonitrile copolymer, acrylonitrile butadiene styrene block copolymers and polyvinyl chloride. So-called blends made from the polymers listed are also preferably used, which the person skilled in the art understands to be a combination of two or more polymers. Particular preference is given to polycarbonate and mixtures containing polycarbonate, very particularly preferably polycarbonate, for example obtained by the phase interface process or the melt transesterification process.

The preferred rubber is at least one from the series of styrene-butadiene rubber, natural rubber, butatidene rubber, isoprene rubber, ethylene-propylene-diene rubber, ethylene-propylene rubber, butadiene-acrylonitrile rubber, hydrogenated nitrile rubber, butyl rubber, Halobutyl rubber, chloroprene rubber, ethylene vinyl acetate rubber, polyurethane rubber, thermoplastic polyurethane, gutta percha, arylate rubber, fluororubber, silicone rubber, sulfide rubber, chlorosulfonyl polyethylene rubber are used. A combination of two or more of the rubbers listed, or a combination of one or more rubber with one or more other plastics is of course also possible.

These thermoplastics or rubbers can be used in pure form or as mixtures with fillers and reinforcing materials, such as glass fibers in particular, as mixtures with each other or with other polymers or as mixtures with conventional polymer additives.

In a preferred embodiment, additives are added to the plastic masses, in particular to the polymer melts and mixtures of polymer melts. These can be added to the extruder as solids, liquids or solutions together with the polymer, or at least some or all of the additives are fed to the extruder via a side stream.

Additives can give a polymer a variety of properties. These can be, for example, colorants, pigments, processing aids, fillers, antioxidants, reinforcing substances, UV Absorbers and light stabilizers, metal deactivators, peroxide scavengers, basic stabilizers, nucleating agents, benzofurans and indolinones that act as stabilizers or antioxidants, mold release agents, flame retardant additives, antistatic agents, colorants and melt stabilizers. Examples of these are carbon black, glass fiber, clay, mica, graphite fiber, titanium dioxide, carbon fibers, carbon nanotubes, ionic liquids and natural fibers.

In the sense of the present invention, an asymmetrical screw cross-sectional profile is characterized in that there is no mirror axis or axis of rotation through any point in the plane of the screw cross-sectional profile with which a screw cross-sectional profile congruent to an initial screw cross-sectional profile can be generated; Preferably there is no mirror axis through any point within a screw cross-sectional profile, particularly preferably no mirror axis through the construction center KP of a screw cross-sectional profile, with which a profile that is congruent with the initial profile can be generated. The design center KP is the point within the screw cross-sectional profile, which is the center of all circular arcs that form combs and grooves. In the context of the present invention, the construction center KP of a screw profile coincides with the rotation center P of this screw profile. For example, EP 0002131 A 1, Fig. 5 (A) or Fig. 5 (B), shows the screw profiles of a pair of screw elements which are asymmetrical in the sense of the present invention. The screw profiles of a pair of screw elements shown in EP 0002131 A1, Fig. 5 (A) or Fig. 5 (B), also have the property that they are not congruent, but they can be converted into one another by axes mirroring and rotation .

A screw cross-sectional profile, also referred to as a screw profile for short in the context of this invention, is understood to mean the outer contour of a screw element in a flat section at right angles to the axis of rotation of the screw element. Rules for generating precisely scraping screw profiles are shown, for example, in [1] ([1] = Klemens Kohlgrüber: “The co-rotating twin-screw extruder”, 2nd edition, Hanser Verlag Munich 2016) on pages 107 to 120. It is also described here that a predetermined screw profile on a first shaft of a twin-screw extruder determines the screw profile on a second shaft of the twin-screw extruder that is immediately adjacent to the first shaft ([1], page 108). The screw profile on the first shaft is therefore referred to as the generating screw profile. The screw profile on the second shaft follows from the screw profile of the first shaft of the twin screw extruder and is therefore referred to as the generated screw profile. Twin-shaft screw machines rotating in the same direction, whose screw shafts scrape each other precisely, have been known for a long time, for example from DE 862 668 C. In polymer production and processing, screw machines with screw shafts, whose screw elements are based on the principle of precisely scraping screw cross-sectional profiles, have a wide range of uses experience. This is primarily due to the fact that polymer melts adhere to surfaces and degrade over time at normal processing temperatures, which is prevented by the self-cleaning effect of screw elements in multi-screw machines that precisely scrape each other in pairs. In a multi-screw extruder, the screw element with the producing screw profile and the screw element with the generated screw profile are always used alternately on adjacent shafts.

A distinction must be made here between two things: the exact scraping snail profd, a mathematical construct in which two snail elements, which lie opposite each other on two immediately adjacent snail edges, scrape each other with a screw element-snail element clearance that approaches zero, and snail profde for material reality intended use, i.e. technically designed screw elements. If the term “exactly scraping” is used in the context of the present invention, it means - unless otherwise stated - the mathematical construct of a precisely scraping screw profile or the corresponding screw element having this screw profile. If the term “practically scraping” or “executed” is used in the context of the present invention, then - unless otherwise stated - the technically executed screw element or its screw profile, whereby this practically scraping screw profile was derived from a precisely scraping screw profile, preferably by using one of the game strategies of increasing the center distance, longitudinal section equidistant, spatial equidistant or circle equidistant, as explained in more detail below.

A person skilled in the field of screw elements naturally understands that a single screw element or screw profd alone cannot be exactly abrasive or practically abrasive, but that a pair of such elements is always required for this.

Modern extruders have a modular system in which various screw elements can be mounted on a core shaft to form a screw flute; Such a snail shaft is therefore segmented. This allows the expert to adapt the extruder to the respective process task. However, a worm shaft can also be made in one piece, i.e. have only one worm element that extends essentially over the entire length of the worm shaft, or it can only be partially segmented. The present invention relates to both Screw elements that can be mounted on a core shaft, as well as on the screw shafts described above, which are made from just one piece.

As is known, multi-screw extruders, in particular twin-screw extruders, introduce mechanical energy into an extrudate through dissipation. This has desirable and undesirable consequences because, on the one hand, the energy input is necessary to fulfill process engineering tasks such as mixing and degassing and, on the other hand, the mechanical energy introduced is consumed and also leads to temperature increases in the extrudate, which can lead to undesirable chemical reactions that damage the extrudate .

As is well known, mixing is also a basic operation in multi-screw extruders, especially twin-screw extruders. Inhomogeneities in the extrudate due to imperfect mixing are known to lead to problems in further processing of the extrudate as well as in the final properties.

Degassing, i.e. the removal of volatile components, is also known to be a basic operation on multi-screw extruders, in particular twin-screw extruders, as described, for example, in [1], pages 494 to 525. For degassing processes, the highest possible efficiency in degassing with low energy input is desirable in order to achieve economically high throughputs and good extmdata quality. Such processes are, in addition to generally described in [1], also, for example, in WO2010139413A1 [2], which describes a device and method for degassing solvent-containing polycarbonate solutions.

For degassing, a polymer is transported as an extrudate in a partially filled section past a degassing opening. Through the opening, volatile components such as by-products, monomers, oligomers, solvents or degradation products of the polymer resulting from polycondensation reactions can be removed under the influence of temperature, water, oxygen or other components. In order to improve the removal of volatile components, the pressure in the degassing opening is reduced compared to the ambient pressure, depending on the degassing task. In [1], pages 494 to 525, it is also described that bubble formation and thus foaming of polymer melts is useful for residual degassing because it creates an inner surface that improves mass transfer. Foaming requires a sufficiently high excess pressure of volatile components in the polymer, about 1 bar. By applying shear to the polymer, bubble formation can be promoted, thereby improving the degassing effect. As is well known, the extrudate in a twin-screw extruder is sheared particularly strongly between a screw comb and the inner wall of the housing bore of an extruder. A particularly large amount of energy is dissipated into the extrudate, which locally leads to severe overheating in the extrudate. This is for example in [1] on pages 416 to 423, pictures 4.80 to 4.84. shown. These local overheats can lead to damage in the extrudate such as changes in smell, color, chemical composition or molecular weight or to the formation of inhomogeneities in the extrudate such as gel bodies or specks. Above all, a large comb angle and in particular a large sum of the comb angles of a pair of screw elements, which lie opposite one another on immediately adjacent screw shafts and thereby scrape each other, is harmful.

Now there is a contradiction between the requirements of degassing or dispersion, both of which require shearing, and the avoidance of damage to the extrudate. It would be advantageous to combine the requirements of degassing or dispersion with those of extrudate protection in such a way that an optimum of degassing or dispersion is achieved with a minimum of damage to the extrudate. Furthermore, it is neither useful for degassing nor for dispersion if the same proportion of a total amount of extrudate is sheared again and again because the exchange of extrudate on the inner wall of the housing bore of an extruder is only small.

The problem of extrudate damage and energy input can be solved, for example, as in WO2009152973A1 [3], in which screw elements for multi-shaft screw machines with pairs of screw shafts in the same direction and pairs of precisely scraped screw shafts, with two or more screw flights Z, with a center distance A and outer diameter DE, whereby the The sum of the comb angles of a pair of screw elements is greater than 0 and less than

and their use are described. Such screw elements are also preferably used in the extruders disclosed in [2]. However, the use of such screw elements does not improve the degassing effect.

US 4131371 A [4] describes eccentric, mutually scraping conveying screw elements that rotate in the same direction, with eccentric profiles whose combs have different distances from the housing. This achieves an even load on the extrudate by spreading it on the wall, thereby providing more surface area for heat and mass transfer. This can improve the degassing effect possibly be achieved. The aspect of wide combs and the associated disadvantages is not discussed.

EP 0002131 A1 [5] describes eccentric, asymmetrical screw elements that practically scrape each other, in which one comb of a respective screw element has a smaller distance from the inner wall of the housing bore of an extruder than the other comb or combs of the respective screw element. The main effect described there is the exchange of material between the extruder housing bores and uniform, intensive shear. These screw elements have Z combs and Z grooves for Z ≥ 2 flights. The clearance between screw element and screw element s - i.e. the distance between the screw profiles of the screw elements of a pair of screw elements that lie opposite one another on two immediately adjacent screw shafts - is not taken into account.

From [5] it can be derived that the sum of the comb angles S WO of each screw element of a pair of screw elements in which the two screw elements scrape each other exactly

is, with numerous mathematically equivalent formulations possible.

It is known to the person skilled in the art and stated, for example, in [1], on pages 39 to 41 and on pages 113 to 121, that technically designed screw elements have games - both screw element-screw element games and screw element-housing wall 5 games to ensure the functionality of the extruder. This is necessary to avoid metal “seizing”, manufacturing tolerances, roughness, angular deviations as well as uneven thermal expansion and excessive extrudate stress due to insufficient distances between two screw elements that are directly adjacent to each other on two immediately adjacent screw shafts. The pages mentioned also explain methods for determining the exact geometry of the element to be manufactured from the games and the precisely scraped contour. These methods are called game strategies.

The game strategies longitudinal equidistant, circular equidistant and spatial equidistant are also referred to below as longitudinal equidistant calculation rules and circular equidistant calculation rules and spatial equidistance calculation rule. Another game strategy is to increase the center distance according to [1], pages 40 and 41.

The spatial equidistance is mentioned, for example, in [1], pages 40 and 41. A spatial equidistance can, for example, be based on a parameter representation of the outer surface of an exact

scraping screw element can be obtained, where a and b stand for parameters that are to be selected according to the equation with which the outer surface of the relevant one is exactly

scraping screw element is described. Below, some examples of what such a parameter representation can look like are described.

For the following considerations, a Cartesian coordinate system is assumed in which the coordinate along the axis of rotation of the extruder is referred to as z and x and y are the coordinates in the plane perpendicular to the axis of rotation, which is this plane at x = 0, y = 0 and z = 0 intersects:

For example, with a pair of screw elements in which the two screw elements lie opposite each other on two immediately adjacent screw shafts and scrape each other exactly, the screw profile of each of the two screw elements can be in the x - y plane, with the respective axis of rotation Axis coincides, and the distance to the axis of rotation r _e (γ) is given as a 2 π periodic function of the screw profile of the angle y to the x-axis, by a representation of the exactly scraped screw element profile according to the following equation (5)

be played back. In such a case, a = y and b = z can be chosen.

Such a pair of screw elements can be formed, for example, as a pair of conveying elements or as a pair of kneading disks.

In order to construct conveyor elements, the screw profile is continued in space helically in the plane in order to obtain the delimiting surface of a precisely scraped screw element. For a screw element with the pitch T the result is, with the z coordinate as an additional parameter

The positive sign stands for a right-handed screw profile, the negative sign for a left-handed screw profile.

With kneading disks, the screw profile is moved into space along the z-axis so that

results.

If a snail profile, for example a precisely scraped snail profile, is built up in sections in the plane via circular arcs i with the center coordinates and the radius

and β is an angle for whose valid values the circular arc represents an exactly scraping snail profile, then the circular arc can pass through

to be discribed. The following then applies to the representation of a delimiting surface of a precisely scraping conveyor element in space

and for the representation of a delimiting surface of a precisely scraping kneading disk accordingly

In a conveyor element, the pitch T of a screw element is the axial length that is required for complete rotation of the screw profile of the screw element. When calculating a screw profile, in which, starting from a pair of screw elements with precisely scraping screw profiles, the space equivalency calculation rule is used to determine the screw profiles of a pair of practically scraping screw elements, taking into account the screw element-screw element clearance s, the following procedure can be carried out, for example, after determining a parameter representation r: To that point

becomes the associated normal vector

formed, whereby the sign is chosen so that

points outwards away from the axis of rotation. The outer surface of the technically designed screw element to be manufactured then results from the

Parameter representation

Further spatial equidistance calculation rules may also be possible according to the invention.

The circular equidistant method also assumes a precisely scraped snail profile in the plane. Starting from the precisely scraped snail profile in the x - y plane, a perpendicular is cut at each point, whereby the direction of the perpendicular is selected so that it points into the interior of the snail profile. The point is s/2 along this perpendicular into the interior of the If the screw profile is shifted, it then belongs to the technically designed screw profile. If a section of a precisely scraped screw profile is a circular arc with radius r _i , the associated section of the associated technically designed screw profile is a circular arc with the same center and radius

This is a circular equidistance calculation rule in the sense of the present invention. Further circular equidistance calculation rules may also be possible according to the invention.

With the methods of longitudinal section equidistants, spatial equidistants and circular equidistants, different surface curves of the technically designed screw profile to be manufactured can overlap, so that for a certain angle starting from the center of rotation P of the screw profile, several points on the screw profile curve are available to choose from. The point that is closer to the center of rotation P is then used to produce the screw profile for the technically feasible screw profile. Various forms can be used to represent the technically executed screw profile to be manufactured, for example tables of coordinates. A preferred method is to specify the distance to the axis of rotation r(y) as a 2π or 360° periodic function of the angle γ to the x-axis through the representation

In all of the methods mentioned, there is also a small increase in the flank angles and a reduction in the comb angle or comb angles compared to the flank angles and the comb angle or comb angles of the precisely scraped screw profile. Using the spatial equidistant method always results in smaller comb angles than using the longitudinal section equidistant method and always results in smaller comb angles than using the circular equidistant method. For a larger gradient, the crest angle for the spatial and longitudinal section equidistant becomes larger; for a gradient towards infinity, the spatial and longitudinal section equidistance go against the circular equidistance, that is, for a gradient towards infinity, the spatial and longitudinal section equidistance calculation rule delivers the same comb angle as the circular equidistance calculation rule.

All methods for determining a technically executed geometry of screw profiles starting from a precisely scraped screw profile - i.e. the game strategies - reduce the size of the screw element compared to a screw element with this precisely scraped screw profile in order to obtain the actually technically feasible geometry of a screw element: a distance is created between the precisely scraping snail profile and the technically designed, practically scraping snail profile. A game strategy is used to determine the game between screw element and screw element s, i.e. the distance between the screw profiles of a pair of screw elements that lie opposite one another on two immediately adjacent screw shafts. This screw element-screw element clearance s between these two screw elements does not have to be constant, but it is preferably constant.

In order to produce a constant play between screw element and screw element when the screw elements are scraped against each other, the spatial equidistance is preferred according to the explanation above.

Large screw element-screw element clearances reduce the energy input into an extrudate because this reduces shear. However, oversized games are snail element snail element s and snail element housings - in technically designed Extruders are also a disadvantage. They lead to reduced scraping of screw elements, which lie opposite each other in pairs on immediately adjacent screw shafts, and worsened exchange of extrudate on the screw elements or the housing bore, thereby increasing the risk that damaged extrudate is created due to a long residence time and gets into the extrudate stream, which leads to This can lead to specks, gels or discoloration, which in turn affects the quality of the desired end product. Excessively large screw element-screw element s and screw element-housing clearances δ also lead to reduced degassing and a reduced mixing effect due to reduced extrudate exchange on the screw surfaces or on the inner wall of the housing bore.

In addition, the influence that can be had on the sum of the comb angles via screw element-snail element s games is limited.

In addition to the screw profile, as is known to those skilled in the art, other variables also play a role in the geometry of a screw element. These are given, for example, in [1] on page 115.

As shown above, the prior art does not show a solution to the problem of how good degassing of the extrudate, which requires high shear, can be achieved in an extruder and at the same time how damage to the extrudate due to excessive energy input can be avoided is a consequence of the high shear, whereby, on the one hand, the exchange of extrudate on the inner wall of the housing bore of an extruder is increased, because otherwise the degassing of the extrudate is only low, and on the other hand, a good mixing effect and dispersion can be achieved.

A good mixing effect is required for good degassing, since degassing takes place primarily from the surface of the extrudate and fresh, not yet degassed extrudate must be transported there in order to enable further degassing. Furthermore, the degassed extrudate should be as homogeneous as possible, which requires a uniform energy input and the avoidance of local overheating.

As is known to those skilled in the art and explained, for example, in [1] on pages 475 to 478, there is a particularly high shear load in the area of the combs near the inner wall of the housing bore, which is conducive to dispersion. This plays a particular role in dispersing solid agglomerates that are used as fillers or reinforcing materials, which is another basic operation on extruders. Frequent replacement of the sheared material is therefore also beneficial for the dispersing effect, as is known to those skilled in the art. However, [1] on page 478 only refers to reduced throughput as a method for better dispersion, which is not preferred for economic reasons. The object of the present invention is therefore to ensure good degassing of an extrudate in an extruder and at the same time - through low energy input - to avoid damage to the extrudate. A further object of the present invention is to additionally ensure good dispersion.

In particular, it is the object of the present invention to provide a pair of screw elements which ensure good degassing of an extrudate in an extruder and at the same time avoid damage to the extrudate. The pair of screw elements should also achieve good dispersion and a good mixing effect. Damage to the extrudate should preferably be avoided by the pair of screw elements ensuring a reduced energy input into the extrudate without impairing the degassing of the extrudate.

Surprisingly, the task is solved by a multi-shaft screw machine with the features of the main claim.

In particular, the task is further solved by a method according to claim 12.

Within the scope of this invention, the following applies:

A helical profile is a closed convex curve. A snail profile is made up of several different curves, which - depending on their geometric properties - are referred to as a “comb”, a “flank” or a “groove”.

The radius of curvature of the screw profile is less than or equal to the center distance and greater than or equal to zero at every point. A zero radius of curvature is equivalent to a kink in the screw profile.

A kink is a location on a screw profile where starting from a parameter representation

with the arc length l as a parameter for a parameter value l _k , it holds that the left-hand and right-hand limits for the values of the functions x(l) and y(l) agree (this is identical to the property that the curve is closed at this point ), so

and the direction vectors of the derivatives of the curve according to the arc length l do not point in the same direction, so their cross product does not disappear:

In the event that two circular arcs do not merge tangentially into one another as part of a screw profile, the kink is located at the intersection of the two circular arcs. It is possible to treat a bend as a circular arc with the center equal to the intersection of the two circular arcs and with zero radius; this is done in the examples.

A curve is a continuous line having a length greater than zero but no width, a curve having a first end point and a second end point that are not one and the same point; that is, the first end point does not coincide with the second end point.

A curve can be composed of several, finitely many curve sections, with a first curve section having a common point of contact with a second curve section which is immediately adjacent to the first curve section.

However, a curve can also consist of exactly one curve section.

A curve may only have a finite number of kinks, which by definition can only occur in the common contact point of two immediately adjacent curve sections of a curve. There can also be a kink in the common contact point of two immediately adjacent curves.

A curve segment is a portion of a curve path, the curve segment having a first end point and a second end point that are not one and the same point; that is, the first end point does not coincide with the second end point.

A curve section is preferably selected from the group comprising the following members: circular arc, elliptical arc, parabolic arc, or a spline or a section of a spline, result of the application of the longitudinal section equidistance calculation rule according to [1], pages 117 to 121 on circular arcs, elliptical arcs or parabolic arcs, or on a spline or on a section of a spline, result of the application of the spatial equidistance calculation rule to circular arcs, elliptical arcs or parabolic arcs, or on a spline or on a section of a spline, or result of the application of the circular equidistance calculation rule, on circular arcs, elliptical arcs, parabolic arcs, or on a spline or on a section of a spline. It also applies to a curve section that it is a line that is in a parameter representation of its arc length l

can be represented and in which x _k,l (l) and y _k,l (l) are analytical functions and x and y are the coordinates of the line in the plane, and can therefore be represented by infinite power series, continuous, can be differentiated as often as desired and therefore kink-free .

A piece is either a curve section or a bend.

A closed, convex curve is an uninterrupted line of non-zero length but no width, composed of one or more curves, which in turn are composed of one or more curve sections. It does not have an excellent starting and ending point. You can determine the length of the curve starting from any point on the curve by adding up the length of the curve sections once around the curve. Any tangent to a closed, convex curve lies outside the area enclosed by the curve.

Since all curve portions of a helical profile are located in a plane, a closed curve, which is a helical profile, divides the area of that plane into an area inside the closed curve and an area outside the closed curve.

A circular arc is a section of curve in which all points of the circular arc have the same distance, called radius, from a common center. An arc has a start and an end point, which are not the same point.

A circular arc is only considered a circular arc if and only if all points of this circular arc have the same center and the same radius and the points of this circular arc form an uninterrupted curve section; that is, two immediately adjacent circular arcs that have a common point of contact are only considered as two circular arcs if they have a different center or a different radius. According to the invention, only circular arcs are used that have a center angle smaller than π in radians.

A circular arc Z is characterized by the coordinates of its center xm _i and ym _i by its radius r _i , by its initial angle β _a,i and its center angle α _i , where the valid values for the angle β in formula (10) are between β _{a ,i} - and β _e,i = β _a,i + α _i (18).

The center of rotation P of a screw profile is the intersection of the axis of rotation X of a screw element with the cross-sectional plane perpendicular to this axis of rotation. The center of rotation P of the screw profile, hereinafter also referred to as the pivot point P or fulcrum, also coincides with the center point M of the housing bore in which the respective screw element is located or for which the respective screw element is designed.

In relation to a screw profile, a pivot point P is the point around which a screw profile rotates as a cross-sectional image of a screw element.

A comb is a curve of a snail profile in which all points of this curve, apart from the common points of contact with the two curve sections immediately adjacent to the comb, are at a greater distance from the pivot point P than the two curve sections immediately adjacent to the comb. According to the invention, the curve that forms a comb is exactly a curve section that is exactly a circular arc with the pivot point P of the screw profile as the center.

According to the invention, all combs of a screw profile are each formed by exactly one circular arc, each of which has the pivot point P of the screw profile as the center.

The comb radius is the distance of the respective comb from the pivot point P of a screw profile.

A groove is a curve of a screw profile in which all points of this curve, apart from the common points of contact with the two curve sections immediately adjacent to the groove, are at a smaller distance from the pivot point P than the two curve sections immediately adjacent to the groove.

According to the invention, the curve that forms a groove is exactly a curve section that is exactly a circular arc with the pivot point P of the screw profile as the center.

According to the invention, all grooves of a screw profile are each formed by exactly one circular arc, each of which has the pivot point P of the screw profile as the center.

A flank is a curve of a screw profile between a comb and a groove that is convex to the center of rotation P, this flank having a common point of contact with the comb and with the groove.

A flank can be a single curve section or composed of several curve sections. The radius of curvature of a flank is less than or equal to the center distance A at every point, preferably smaller than the center distance A. According to the invention, the mathematical expressions which form the basis of a curve section of a flank are preferably selected from the group of mathematical expressions comprising the following members: circular arc, result of the application of the longitudinal section equidistance calculation rule according to [1], pages 117 to 121 to a circular arc with a radius of curvature smaller than center distance A or equal to center distance A of a precisely scraping snail profile composed only of circular arcs, result of the application of the spatial equidistance calculation rule to a circular arc with a radius of curvature smaller than center distance A or equal to center distance A of an exactly scraping snail profile composed only of circular arcs and result of the application of the circular equidistance calculation rule a circular arc with a radius of curvature smaller than center distance A or equal to center distance A of a precisely scraped screw profile composed only of circular arcs.

Components of the pair of screw elements according to the invention or the associated screw profiles can be provided with index characters such as n, m, or i, or with natural numbers in order to be able to distinguish these components from one another if these components can occur multiple times.

Furthermore, within the scope of the present invention:

Table 1: Parameters for representing a screw profile

If it is explained in the context of the present description that a value is “selected” for a size, as is the case, for example, with the pitch T, the clearance between the screw element and the housing wall 8, the clearance between the screw element and the screw element s, or the additional gap SP , this does not mean that this quantity can be assigned any value when obtaining screw profiles for a pair of screw elements that should be usable as intended. A person skilled in the field of designing screw elements for extruders can estimate or determine through CFD simulations what values these variables have for a given extruder depending, for example, on the viscosity of the extrudate at the processing temperature, the desired degree of filling of the extruder, the desired energy input into the extruder Extrudate or the speed of the shafts, must be assigned sensibly. Especially if such a value was obtained through assessment, it is usually necessary to confirm it or determine it more precisely through simulations; this is usually done iteratively. By selecting the additional gap SP, the mass transfer on the inner wall of the housing and the mixing effect can be adjusted. By appropriately selecting S, the maximum shear can be set and with ƒ the comb angle and thus the length over which the maximum shear between the comb and the housing should act can be set.

(1) In particular, the tasks according to a first embodiment of the invention are solved by: a pair of screw elements, suitable for a multi-shaft screw machine with m screw shafts SWi to SW _m rotating in the same direction and at the same speed, whose respective adjacent axes of rotation X ₁ to X _m are rectangular in a cross section to the axes of rotation have a center distance A and with m interpenetrating, circular housing bores, each of which has an identical housing bore inner diameter D and whose bore centers M ₁ to M _m have a distance that is equal to the axis distance A, and whose bore centers M ₁ to M _m _coincide with the respective axes _of _rotation _X ₁ _to Screw elements scrape each other with a screw element-screw element clearance s, with both screw elements having an asymmetrical screw profile, with both screw elements each having exactly two combs, with each of the two screw elements having its two combs at different distances from the respective center of rotation P of the screw profile , whereby one comb has a distance D / 2 reduced by a clearance between the screw element and the housing wall 5 and further reduced by an additional gap SP to the respective center of rotation P and the other comb has a distance D / 2 reduced by a clearance between the screw element and the housing wall 5, not but reduced by an additional gap SP, to the respective center of rotation P, the play between the screw element and the housing wall 5 being the same for both screw elements and the additional gap SP being the same for both screw elements, the sum of the comb angles BKW of the combs of both screw elements being greater in radians is as 0 and for the factor ƒ with ƒ = BKW / BKGW (19) it applies that the factor / is greater than 0 and less than or equal to 0.95, where BKW is the sum of the comb angles in radians of both screw elements and BKGW is determined by:

The same games of screw element housing wall 8 or the same additional column SP have the advantage of a uniform energy input.

(2) Preferably / is greater than or equal to 0.1 and less than or equal to 0.8 and particularly preferably f is greater than or equal to 0.2 and less than or equal to 0.6.

This preferred embodiment of the invention represents a second embodiment after the first embodiment presented above.

(3) It is preferred that the ratio of the screw element-screw element clearance s between the two screw elements of a pair of screw elements to the housing bore inner diameter D is from 0.002 to 0.05, preferably from 0.003 to 0.03 and particularly preferably from 0.005 to 0.02 .

This preferred embodiment of the invention represents a third embodiment after the first or second embodiment shown above.

(4) It is further preferred that the clearance between the screw element and the housing wall 5, based on the housing bore inner diameter D, is 0.002 to 0.05, preferably from 0.003 to 0.03 and particularly preferably from 0.005 to 0.02. This particularly preferred embodiment of the invention represents a fourth embodiment according to one of the embodiments presented above.

(5) It is further preferred that the additional gap SP, based on the flight depth GT of the respective screw element, is from 0.015 to 0.4, preferably from 0.02 to 0.3 and particularly preferably from 0.025 to 0.25.

This particularly preferred embodiment of the invention represents a fifth embodiment according to one of the embodiments presented above.

(6) Further preferably, the comb angles of the combs of the pair of screw elements, which have the screw element-housing wall clearance δ, but not the additional gap SP, between the housing bore inner wall, are the same.

This further preferred embodiment of the invention represents a sixth embodiment according to one of the embodiments presented above.

(7) Furthermore, more preferably, the comb angles of the combs of the pair of screw elements, which have the screw element-housing wall clearance δ and the additional gap SP between the housing bore inner wall, are the same.

This further preferred embodiment of the invention represents a seventh embodiment according to one of the embodiments presented above.

(8) It is additionally preferred that for both screw elements of the pair of screw elements, the comb angles of the combs of the screw elements of the pair of screw elements, which have the clearance between the screw element and the housing wall 5 and the additional gap SP, are larger than the comb angles of the combs Screw elements of the pair of screw elements, which have the clearance between the screw element and the housing wall 5, but not the additional gap SP.

This additionally preferred embodiment of the invention represents an eighth embodiment according to one of the embodiments presented above.

(9) Very particularly preferably, the screw profiles of the pair of screw elements are not congruent, with the screw profiles of the two screw elements being able to be converted into one another by mirroring the axes and rotating them.

This very preferred embodiment of the invention represents a ninth embodiment according to one of the first to eighth embodiments shown above. The fact that the screw profs of the two screw elements can be transferred into one another through an axis mirroring and a rotation ensures that the energy input into each of the two screw elements of a pair of screw elements is the same. This has proven to be advantageous because it avoids local overheating of the extrudate when the pair of screw elements according to the invention is used as intended.

(10) It is also preferred that each of the two screw profiles of the pair of screw elements has exactly two (2) grooves and has exactly four (4) flanks.

This very preferred embodiment of the invention represents a tenth embodiment according to one of the first embodiments shown above.

(11) It is also preferred that the two screw profiles of the pair of screw elements have exactly four (4) grooves and exactly eight (8) flanks.

This very preferred embodiment of the invention represents an eleventh embodiment according to one of the tenth embodiments shown above.

The pair of screw elements according to the invention can be formed as a pair of conveying elements or as a pair of kneading disks; according to the invention it is preferably designed as a pair of conveying elements.

The present invention also relates to a multi-shaft screw machine which has the pair of screw elements according to the invention.

The present invention also relates to a method for producing or processing an extrudate using the pair of screw elements according to the invention in a multi-shaft screw machine. The extrudate is preferably a plastic or viscoelastic mass, particularly preferably a polymer melt, in particular a melt of a thermoplastic or an elastomer, most particularly a melt of a polycarbonate or a polyester carbonate or a thermoplastic polyurethane or a rubber. The method preferably includes the steps:

(1) Providing a multi-screw screw machine comprising a pair of screw elements according to the invention;

(2) Making or processing an extrudate. The present invention furthermore relates to a method for producing the screw profiles of the screw elements of the pair of screw elements according to the invention, starting from a precisely scraped screw profile according to the prior art.

The screw profiles of a pair of screw elements according to the invention can be generated, for example, as explained below, starting from an existing extruder with values for the center distance A and the housing bore inner diameter D specified by it, each of the two screw elements having exactly two combs and the two screw elements of a pair Snail elements are referred to as left and right snail elements, with formula symbols with subscript l or r.

In order to calculate the values of the screw elements for producing the screw profiles of a pair of screw elements according to the invention, both the values of sizes of a pair of screw elements that scrape each other exactly and the values of sizes of a pair of screw elements that practically scrape each other are used, the values of the sizes of a pair of screw elements that practically scrape each other Pair of screw elements depend on the values of the sizes of a pair of screw elements that scrape each other exactly and can be calculated from them according to Table 1.

(I) In a first step, the value for the clearance between the screw element and the screw element s and the value for the clearance between the screw element and the housing wall δ are selected, which should apply to the executed screw element.

(II) In a second step, the value for the outer radius RE of a precisely scraped screw profile is determined according to the equation:

RE = DE/2 (21) with

DE = D — 2δ + s (22)

(III) In a third step, the value for the inner radius RI of a precisely scraped screw profile is determined according to the equation:

(IV) In a fourth step, the outer radius RA of a technically feasible/usable screw element is determined according to the equation:

RA = D/2 - δ (24)

(V) In a fifth step, the inner radius RK of a technically feasible/usable screw element is determined according to the equation:

RK = A - D/2 + δ — s (25)

(VI) In a sixth step, the flight depth of a technically feasible / intended use screw element is determined according to the equation

GT = RA - RK (26) calculated.

(VII) In a seventh step, a value is selected for the additional gap SP of a technically feasible/intended screw element, whereby SP < GT/2 is always the case.

Steps (II) to (V) can be carried out in any order.

(VIII) In an eighth step, the initial sum of the comb angles SKWO of the respective screw element is determined according to equation (4) or (27) for each of the two screw elements of a pair of screw elements that scrape each other exactly:

(IX) In a ninth step, the sum of the comb angles of a pair of screw elements BSKW0 that scrape each other exactly is calculated according to BSKW0 = 2 g SKW0 (28) where the factor g is chosen, where g is greater than 0.1 and less than 0.95, preferably greater than 0.15 and less than 0.8 and particularly preferably greater than 0.2 and less than 0.6.

(X) In a tenth step, the comb angle KW0 _{l, δ} of the precisely scraped Profd of the left screw element and the comb angle KW0 _{r, δ} of the right screw element are determined for the comb of the respective screw element that has the play Screw element housing wall 5 to the inner wall of the housing bore, marked with a subscript 5 in formula symbols, but not the additional gap SP, in such a way that the following applies to the sum of the comb angles of these combs:

KW0 _l,δ + KW0 _r,δ < BSKW0 (29) preferred

and particularly preferred

where all comb angles are greater than 0.

(XI) In an eleventh step, the comb angle KW0 _{l, δ + SP} of the screw profile of the left screw element and the comb angle KW0 _{r, δ + SP} of the right screw element are determined for the comb of the respective screw element for a pair of screw elements that scrape each other exactly, which respectively the clearance between the screw element housing wall 5 and the gap SP, i.e. S + SP, is marked with a subscript S + SP in formula symbols, in such a way that the following applies to the sum of the comb angles of these combs:

KW0 _l,δ+SP + KW0 _r,δ+SP = BSKW0 - KW0 _l,δ + KW0 _r,δ ) (32) and preferred

KW0 _l,δ+SP + KW0 _r,δ+SP = 2 KW0 _δ+SP = BSKW0 - KW0 _l,δ + KW0 _r,δ ) (33) (XII) In a twelfth step, for a pair of screw elements that scrape each other exactly, the screw profile of the first screw element, here selected as the left screw element - the right screw element could also be selected, consisting of the curves mentioned below, is constructed. These curves follow one another directly in a direction of rotation as indicated below, whereby the direction of rotation can be mathematically positive or negative, and the curves merge into one another at their respective end points. This screw profile for the first screw element represents the generating screw profile. - A circular arc with radius RE, with the angle KW0 _l,δ and with the center of rotation P of the screw profile as the center, whereby this circular arc is the first comb - A first flank [Flank 1 ]; - A circular arc with radius RI, with the angle KW0 _r,δ and with the center of rotation P of the screw profile as the center, this circular arc being the first groove; - A second edge [edge 2]; - A circular arc with radius RE — SP, angle KW0 _l,δ+SP and center of rotation center P of the screw profile, which is the second comb; - A third edge [edge 3]; - A circular arc with radius RI + SP, angle KW0 _l,δ+SP and center of rotation center P of the screw profile, this circular arc being the second groove; - A fourth flank [Flank 4], which closes the profile between the second groove and the first ridge.

(XIII) In a thirteenth step, for a pair of screw elements that scrape each other exactly, the screw profile of the second screw element, here selected as the right screw element, is constructed. For this purpose, the pivot point of the left screw element is set to the coordinates x = 0 and y = 0 and the pivot point of the right screw element is set to the coordinates x = A and y = 0. The screw profile of the left screw element is geometrically divided into its curve sections and - if available - Kinks i = 1. . n decomposed. The precisely scraped screw profile of the right screw element then becomes the Snail profile of the left snail element corresponding curve sections and - if present - kinks, named i' = 1. . n.

For a curve section i in a parameter representation

with p _a,i ≤ p ≤ p _e,i , where the derivative of the analytic functions x _i (p) and y _i (p) do not become zero for the same value and where it is assumed, without loss of generality, that

with increasing p winds around the pivot point in a mathematically positive sense, a standardized normal vector

formed, whereby the sign is chosen so that the normal vector points out of the profile, away from the pivot point.

Each curve section is assigned a starting angle β _a,i and an end angle β _e,i . The initial angle satisfies the condition at p = p _a

and the final angle from the components of the normal vector at p = p _e

where β _e,i > β _a,i and β _e,i < β _a,i + π.

The curve section i on the left snail then corresponds to a curve section i' on the right snail with the coordinate representation

In a preferred embodiment, the curve section i represents a circular arc with the parameter representation (39)

with β _a,i ≤ β ≤ β _e,i , then is the normalized normal vector

and the representation of the corresponding circular arc is

with r _i' = A — r _i' xm _i' = xm _i' + A and ym _i' = ym _i and (as above) β _a,i ≤ β ≤ β _e,i .

If the curve section represents a circle with X = A, then r _i' = 0. and the corresponding section is a bend.

If the piece i represents a bend with the coordinates, then this corresponds to a circular arc with radius , the representation of which can be obtained from the above formula with r _i' = A.

In a preferred embodiment, the screw profile of the screw elements according to the invention is derived from a precisely scraped screw profile by using the axial distance increase, the circular equidistant, the longitudinal equidistant or the spatial equidistant, the sum of the comb angles BKW of the combs of both screw elements being greater than 0 in radians and for the factor ƒ with ƒ = BKW / BKGW (42) it applies that the factor ƒ is greater than 0 and less than or equal to 0.95, where BKW is the sum of the comb angles in radians of both screw elements and BKGW is determined by:

In a further preferred embodiment, the screw profile of the screw elements according to the invention is composed of curve sections which are selected from the group of mathematical expressions comprising the following members: circular arc, elliptical arc, parabolic arc, spline or section of a spline, result of the application of the longitudinal section equidistance calculation rule according to [1] , pages 117 to 121 on circular arcs, elliptical arcs, parabolic arcs or on a spline or on a section of a spline, result of applying the spatial equidistance calculation rule to circular arcs, elliptical arcs, parabolic arcs or on a spline or on a section of a spline, or result of applying the circular equidistance calculation rule , on a circular arc, elliptical arc, parabolic arc or on a spline or on a section of a spline.

In a further preferred embodiment, at least two pairs of screw elements according to the invention are arranged axially directly one behind the other in a multi-shaft screw machine. Such an arrangement is basically shown, for example, in PCT/EP2021/078863, where PCT/EP2021/078863 describes in particular pairs of screw elements that precisely clean one another, whereas the present invention relates to screw elements that practically scrape off.

1 shows the practically scraped screw profile of the left screw element from Example 2 to illustrate the geometric dimensions.

The invention is explained below using examples, without the invention being restricted to these examples.

Example 1 (comparative example - not according to the invention) Example 1, which is not according to the invention, is a pair of two practically scraping each other

Snail elements with and after

EP 0002131 A1, Fig. 5(A) and Fig. 5(B), whereby the spatial equidistance calculation rule is additionally applied to the screw profile according to EP 0002131 A1, Fig. 5(A) or Fig. 5(B). The screw profiles of the screw elements are asymmetrical, not congruent, but they can be converted into one another by mirroring the axes and rotating them.

The precisely scraped screw profile of the left screw element consists of the pieces i = 1 to 12, which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₁ of the left screw profile based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point of the left screw profile P ₁ based on the housing bore inner diameter D are given in Table 2. The crests of the practically scraping snail profile are the circular arcs 1 and 7. Kinks can be recognized by the fact that the value is.

Table 2: Circular arcs of the precisely scraped profile of the left screw profile of Example 1.

The precisely scraped screw profile of the right screw element consists of the pieces i = T to 12', which are either circular arcs or bends. Table 3 shows the starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₂ of the right screw profile based on the Housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₂ of the right screw profile based on the housing bore inner diameter D. The crests of the practically scraping snail profile are the circular arcs 4' and 10'. Kinks can be recognized by the fact that the value is.

Table 3: Circular arcs of the precisely scraped screw profile of the right screw element from Example 1.

The sum of the comb angles of both precisely scraped screw profiles of the pair of screw elements together is BKW0 = 1.72356 in radians (98.75 °).

The technically designed, practically scraping, screw elements of the pair of screw elements according to Example 1 with screw profiles, which are derived from precisely scraping screw profiles, are asymmetrical, not congruent, but can be moved into one another by mirroring the axis and rotating. The sum of the comb angles of the practically scraping screw profile of a single screw element is 0.73115 radians (41.89 degrees). The sum of the comb angles of the screw profiles of the pair of screw elements in radians is BKW = 1.462 (83.78 °).

The limit value for the sum of the comb angles of the pair of screw elements, calculated according to formula (2), is BKGW = 1.444 (82.71°). This means BKW > BKGW, their ratio

and therefore this pair of screw elements is not according to the invention.

The practically scraping screw profiles of the two screw elements are shown in FIG. 2, together with the associated precisely scraping screw profiles from which the practically scraping screw profiles were derived. Table 4 shows the screw profile of the left screw element in the plane according to formula (13), i.e. the radius as a function of the angle γ _l starting from the center of rotation P ₁ of the left screw element. The radii are each given for an angular distance of two degrees, except when transitioning into a ridge or groove area, where additional points are given. Table 5 gives the corresponding coordinates of the screw profile of the right screw element starting from the center of rotation P ₂ of the right screw element. Fig. 3 shows the pair of screw elements not according to the invention in a top view.

Table 4: Screw profile of the left screw element of the pair not according to the invention

Screw elements from example 1.

Table 5: Screw profile of the right screw element of the pair of screw elements not according to the invention from Example 1.

Example 2 (according to the invention)

Example 2 according to the invention is a pair of two screw elements that practically scrape each other with and so on

the same values for the corresponding quantities as in Example 1, whereby the spatial equidistance calculation rule is also applied. The screw profiles of the screw elements are asymmetrical, not congruent, but they can be converted into one another by mirroring the axes and rotating them.

The precisely scraped screw profile of the left screw element consists of the pieces i = 1 to 20, which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point of the left screw profile P ₁ based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₁ of Left screw profile based on the housing bore inner diameter D are given in Table 6. The crests of the precisely scraped snail profile are the circular arcs 1 and 11. Kinks can be recognized by the fact that the value is.

The precisely scraped screw profile of the right screw element consists of the circular arcs i = 1' to 20', which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₂ of the right screw profile based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₁ of the right screw profile based on the housing bore inner diameter D are given in Table 7. The combs of the practically scraping snail profile are the Circular arcs 6' and 16'. The sum of the comb angles of both precisely scraped screw profiles of the pair of screw elements is BKW0 = 0.8784 in radians (50.32°).

Table 6: Circular arcs of the precisely scraped screw profile of the left screw element from Example 2.

Table 7: Circular arcs of the precisely scraped screw profile of the right screw element from Example 2.

The technically designed, practically scraping, screw elements of the pair of screw elements according to Example 2 with screw profiles, which are derived from precisely scraping screw profiles, are asymmetrical, not congruent, but can be moved into one another by mirroring the axis and rotating. The sum of the comb angles of the practically scraping screw profile of a single screw element is 0.3384 radians (19.30°). The sum of the comb angles of the screw profiles of the pair of screw elements is BKW = 0.6769 in radians (38.78°). The limit value for the sum of the comb angles of the pair of screw elements calculated according to formula (2) is (as in example 1) BKGW = 1.444 in radians (82.71°). This means that BKW < BK GW, the ratio , and this pair of screw elements is

according to the invention.

The practically scraping screw profiles of the pair of screw elements according to the invention are shown in FIG. 4, together with the associated precisely scraping screw profiles from which the practically scraping screw profiles were derived. Table 8 shows the screw profile of the left screw element according to formula (5), i.e. the radius as a function of the angle γ _l starting from the center of rotation P ₁ of the left screw element. The radii are each given for an angular distance of two degrees, except when transitioning into a ridge or groove area, where additional points are given. Table 9 gives the corresponding coordinates of the screw profile of the right screw element. FIG. 5 shows the pair of screw elements according to the invention in a top view.

Table 8: Screw profile of the left screw element of the pair of screw elements according to the invention from Example 2.

Screw elements from Example 2. Example 3 (according to the invention)

Example 3 according to the invention is a pair of two mutually practically scraping screw elements with and , whereby the

Spatial equidistance calculation rule was applied. The screw profiles of the screw elements are asymmetrical, not congruent, but they can be converted into one another by mirroring the axes and rotating them.

The precisely scraped screw profile of the left screw element consists of the pieces i = 1 to 20, which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₁ of the left screw profile based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₁ of the Left screw profile based on the housing bore inner diameter D are given in Table 10. The crests of the precisely scraped snail profile are the circular arcs 1 and 11. Kinks can be recognized by the fact that the value = 0. The combs of the practical

The circular arcs 1 and 11 of the scraping screw profile are.

Table 10: Circular arcs of the exactly scraped profile of the left screw profile from Example 3.

The precisely scraped screw profile of the right screw element consists of the circular arcs i = 1' to 20', which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₁ of the right screw profile based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₁ of the Right screw profile based on the housing bore inner diameter D are given in Table 11. The crests of the precisely scraped profile are the circular arcs 6' and 16'. The sum of the comb angles of both precisely scraped profiles is BKW0 = 0.7716 in radians (44.21°)

Table 11: Circular arcs of the exactly scraped profile of the right screw profile from Example 3.

The technically designed, practically scraping screw elements of the pair of screw elements according to the invention according to Example 3 with screw profiles, which are derived from precisely scraping screw profiles, are also asymmetrical, not congruent, but they can be moved into one another by axes mirroring and rotation. The sum of the comb angles for both the left and right screw profiles is 0.3464 radians (20.89 °), the sum of the comb angles of the pair of screw elements is therefore BKW = 0.6928 (41.78 °).

The limit value for the sum of the comb angles of the pair of screw elements, calculated according to formula (2), is BKGW = 1.848 in radians (105.86 °). This means that BKW < BKGW, the ratio , and the pair of screw elements is according to the invention.

The practically scraping screw profiles of the pair of screw elements according to the invention are shown in FIG. 6, together with the associated precisely scraping screw profiles from which the practically scraping screw profiles were derived. Table 12 shows the screw profile of the left screw element according to formula (5), i.e. the radius as a function of the angle starting from the center of rotation P ₁ of the left screw profile. The radii are each given for an angular distance of two degrees, except when transitioning into a ridge or groove area, where additional points are given. Table 13 gives the corresponding screw profile coordinates of the right screw profile. Fig. 7 shows the pair of screw elements according to the invention in a top view.

Table 12: Screw profile of the left screw element of the pair of screw elements according to the invention from Example 3.

Table 13: Screw profile of the right screw element of the pair of screw elements according to the invention from Example 3.

Example 4 (according to the invention)

Example 4 according to the invention is a pair of two screw elements that practically scrape each other with A/D = 0.84, T/D = 0.75, δ/d = 0.005 and s/D = 0.01, whereby the spatial equidistance calculation rule is also carried out . The screw profiles of the screw elements are asymmetrical, not congruent, but they can be moved into one another by mirroring the axes and rotating them.

The precisely scraped screw profile of the left screw element consists of the pieces i = 1 to 20, which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₁ of the left screw profile based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₁ of the Left screw profile based on the housing bore inner diameter D are given in Table 14. The crests of the precisely scraped snail profile are the circular arcs 1 and 11. Kinks can be recognized by the fact that the value = 0.

Table 14: Circular arcs of the practically scraping screw profile of the left screw element from Example 4.

The precisely scraped screw profile of the right screw element consists of the circular arcs i = 1' to 20', which are either circular arcs or bends. The arc angle, starting angle, end angle, arc radius based on the housing bore inner diameter D, x coordinate of the center of the circular arc i relative to the pivot point P ₁ of the right screw profile based on the housing bore inner diameter D and y coordinate of the center of the circular arc i relative to the pivot point P ₁ of the Right screw profile based on the housing bore inner diameter D are given in Table 15. The crests of the precisely scraped snail profile are the circular arcs 6' and 16'. The sum of the comb angles of both precisely scraped screw profiles of the pair of screw elements together is BKW0 = 0.69814 in radians (40°).

Table 15: Circular arcs of the precisely scraped screw profile of the right screw element from Example 4.

The technically designed, practically scraping screw elements of the pair of screw elements according to the invention according to Example 4 with screw profiles, which are derived from precisely scraping screw profiles, are also asymmetrical, not congruent, but they can be moved into one another by axes mirroring and rotation. The sum of the comb angles for both the left and right screw profiles is 0.25885 radians (14.83°), the sum of the comb angles of the pair of screw elements is BKW = 0.51766 (29.66°). The limit value for the sum of the comb angles of the pair of screw elements, calculated according to formula (2), is BKGW=1.5703 in radians (89.97°). This means that BKW < BKGW

their ratio and the pair of snail egg elements is according to the invention.

The practically scraping screw profiles of the pair of screw elements according to the invention are shown in FIG. 8, together with the associated precisely scraping screw profiles from which the practically scraping screw profiles were derived. Fig. 9 shows the pair of screw elements according to the invention in a top view.

Table 16 shows the screw profile of the left screw element according to formula (5), i.e. the radius as a function of the angle γ _l starting from the center of rotation P ₁ of the left screw profile. The radii are each given for an angular distance of two degrees, except when transitioning into a ridge or groove area, where additional points are given. Table 17 gives the corresponding screw profile coordinates of the right screw profile.

Table 16: Screw profile of the left screw element of the pair according to the invention

Screw elements from Example 4.

Table 17: Screw profile of the right screw element of the pair of screw elements according to the invention from Example 4.

Short description of the figures and list of reference symbols

Figure 1

Practically scraping screw profile of the left screw element from example 2

1. 1 Housing bore inner wall profile of the left part of the housing bore

1.2 Gear depth GT

1.3 Housing bore inner diameter D

1.4 Comb angle of the left screw element, which has a clearance between the screw element and the housing wall 8, but not an additional gap SP: KW _{l, δ}

1.5 Clearance between screw element and housing wall δ

1.6 Gear depth reduced by the additional gap: GT — SP

1.7 The clearance between the screw element and the housing wall is increased by the additional gap: δ + SP

1.8 Comb angle of the left screw element, which has both a clearance between the screw element and the housing wall δ and an additional gap SP: KW _l,δ+SP

1.9 Center of rotation P

Figure 2

Screw profiles of the pair of screw elements not according to the invention from Example 1

2. 1 housing bore inner wall profile

2.2 Profile left screw element, precisely scraped

2.3 Profile left screw element, practically scraped off

2.4 Profile of the right screw element, scraped precisely

2.5 profile right screw element, practically scraped off Figure 3

Top view of the pair of screw elements from Example 1, which are not according to the invention

3.1 Housing bore inner wall profile

3.3 Profile left screw element, practically scraped off

3.5 profile right screw element, practically scraped off

Figure 4

Screw profiles of the pair of screw elements according to the invention from Example 2

4. 1 housing bore inner wall profile

4.2 Profile left screw element, scraped exactly

4.3 Profile left screw element, practically scraped off

4.4 Profile of the right screw element, scraped precisely

4.5 Profile right screw element, practically scraped off

Figure 5

Top view of the pair of screw elements according to the invention from Example 2

5.1 Housing bore inner wall profile

5.3 Profile left screw element, practically scraped off

5.5 Profile right screw element, practically scraped off

Figure 6

Screw profiles of the pair of screw elements according to the invention from Example 3

6. 1 housing bore inner wall profile

6.2 Profile left screw element, precisely scraped

6.3 Profile left screw element, practically scraped off 6.4 Profile of the right screw element, scraped precisely

6.5 Profile right screw element, practically scraped off

Figure 7

Top view of the pair of screw elements according to the invention from Example 3

7. 1 housing bore inner wall profile

7.3 Profile left screw element, practically scraped off

7.5 Profile right screw element, practically scraped off

Figure 8

Screw profiles of the pair of screw elements according to the invention from Example 4

8.1 Housing bore inner wall profile

8.2 Profile left screw element, precisely scraped

8.3 Profile left screw element, practically scraped off

8.4 Profile of the right screw element, scraped precisely

8.5 Profile right screw element, practically scraped off

Figure 9

Top view of the pair of screw elements according to the invention from Example 4

9. 1 housing bore inner wall profile

9.3 Profile left screw element, practically scraped off

9.5 Profile right screw element, practically scraped off

Claims

Patent claims

1. Multi-shaft screw machine, which has a pair of screw elements, with m screw shafts SWi to _SWm rotating in the same direction and at the same speed, the adjacent axes of rotation X ₁ to , each of which has an identical housing bore inner diameter D and whose bore centers M ₁ to M _m have a distance that is equal to the center distance A, and whose bore centers M ₁ to M _m with the respective associated axes of rotation X ₁ to X _m of the worm shafts SWi to SWm and coincide with the centers of rotation P ₁ to P _m of the screw elements, the two screw elements of the pair of screw elements lying opposite one another on immediately adjacent screw shafts, the two screw elements of the pair of screw elements scraping each other with a play of screw element-screw element s, both screw elements having an asymmetrical Have a screw profile, with both screw elements each having exactly two combs, with each of the two screw elements having different distances from the respective center of rotation P of the screw profile, with each comb having a distance D /2 reduced by a clearance between the screw element and the housing wall 5 and further reduced by an additional gap SP to the respective center of rotation P and the other comb has a distance D/2 reduced by a play between the screw element and housing wall 5, but not reduced by an additional gap SP, to the respective center of rotation P, with both Screw elements, the clearance between screw element and housing wall δ is the same and the additional gap SP is the same for both screw elements, characterized in that the sum of the comb angles BKW of the combs of both screw elements is greater than 0 in radians and for the factor ƒ with ƒ = BKW / BKGW (44) applies that the factor ƒ is greater than 0 and less than or equal to 0.95, where BKW is the sum of the comb angles in radians of both screw elements and BKGW is determined by:

wherein the aforementioned parameters are defined as set out in the description. 2. Multi-shaft screw machine according to claim 1, wherein / is greater than or equal to 0.1 and less than or equal to 0.8, preferably f is greater than or equal to 0.2 and less than or equal to 0.6. 3. Multi-shaft screw machine according to claim 1 or claim 2, wherein the ratio of the screw element-screw element clearance s between the two screw elements of a pair of screw elements to the housing bore inner diameter D is from 0.002 to 0.05, preferably from 0.003 to 0.03 and particularly preferably from 0.005 to 0.02. 4. Multi-shaft screw machine according to one of the preceding claims, wherein the play between the screw element and the housing wall 8 based on the housing bore inner diameter D is 0.002 to 0.05, preferably from 0.003 to 0.03 and particularly preferably from 0.005 to 0.02. 5. Multi-shaft screw machine according to one of the preceding claims, wherein the additional gap SP based on the flight depth GT of the respective screw element is from 0.015 to 0.4, preferably from 0.02 to 0.3 and particularly preferably from 0.025 to 0.25 . 6. Multi-shaft screw machine according to one of the preceding claims, wherein the comb angles of the combs of the pair of screw elements which determine the game of screw element Housing wall 5, but not the additional gap SP, to the housing bore inner wall, are the same. 7. Multi-shaft screw machine according to one of the preceding claims, wherein the comb angles of the combs of the pair of screw elements, which have the clearance between the screw element and the housing wall 5 and the additional gap SP to the housing bore inner wall, are the same. 8. Multi-shaft screw machine according to one of the preceding claims, wherein for both screw elements of the pair of screw elements it applies that the comb angles of the combs of the screw elements of the pair of screw elements, which have the clearance between the screw element and the housing wall 5 and the additional gap SP, are larger than the comb angles of the Combs of the screw elements of the pair of screw elements, which have the clearance between the screw element and the housing wall 5, but not the additional gap SP. 9. Multi-shaft screw machine according to one of the preceding claims, wherein the screw profiles of the pair of screw elements are not congruent, the screw profiles of the two screw elements being able to be converted into one another by an axis mirroring and a rotation. 10. Multi-shaft screw machine according to one of the preceding claims, wherein each of the two screw profiles of the pair of screw elements has exactly two (2) grooves and has exactly four (4) flanks. 11. Multi-shaft screw machine according to one of the preceding claims, wherein the two screw profiles of the pair of screw elements have exactly four (4) grooves and have exactly eight (8) flanks. 12. A method for producing or processing an extrudate using a multi-screw machine according to any one of claims 1 to 11, the method comprising the steps:

(1) Providing the multi-shaft screw machine;

(2) Making or processing the extrudate.